Request PDF on ResearchGate | A Plastic-Damage Model for Concrete | In behavior is represented using the Lubliner damage-plasticity model included in. behavior of concrete using various proposed models. As the softening zone is known plastic-damage model originally proposed by Lubliner et al. and later on. Lubliner, J., Oliver, J., Oller, S. and Oñate, E. () A Plastic-Damage Model for Concrete. International Journal of Solids and Structures, 25,
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The hardening parameters and are the equivalent plastic strains under tension and compression, respectively, defined as [ 117 ] where and are the tensile and compressive equivalent plastic strain rates, respectively.
The form taken by tho proposed yitld surface on ditrcrcnt planes of the stress space is shown in Fig. To couple the damage to the plasticity, the damage parameters are introduced into the plastic yield function by considering a reduction in the plastic hardening rate. Bcinnt and Plastic-eamage View at Google Scholar V. According to Faria et al. The plastic yield function is usually expressed by a function of the stress tensor and plastic hardening function, so the damage parameters are included in the plastic yield function with the introduction of the reduction factor in the plastic hardening function.
Comparison of the model predictions with the experimental results under biaxial compression: Numerous improvements to these yield criteria have been proposed in recent years: As shown in Figure 6the strength softening and stiffness degrading, as well as the irreversible strains upon unloading, can be clearly seen under both cyclic uniaxial tension and compression. The model presented in this work is thermodynamically consistent and is developed using internal variables to represent the material damage state.
The practical significance of our results is that plasticity theory is a rather simple model in lub,iner with models based on fracture mechanics or the more sophisticated versions of continuum damage mechanics. Desmorat, Engineering Damage Mechanics: Comparison of 10 quadrilateral finite elrments for plasticity problems.
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Because the associative flow rule is adopted in the present model, the concretr yield function is also used as the plastic potential to obtain the plastic strain. Typical values range from about 0. In this case, considering and in the damage criterion and the plastic yield function, the initial damage thresholds and can be determined as follows: A possible form is [ 44 k t7. All of the parameters can be identified from the uniaxial tension and compression tests. Some of these limitations could bo avoided if a single constitutivc model could be used that governs the non-linear behnvior of concrete.
The plasticity part is based on the true stress using a yield function with two hardening variables, one for the tensile loading history and the other plsatic-damage the compressive loading history. The plasticity part is based on the true stress using dor yield function with tensile and compressive hardening functions.
Concerte conseyucnces of the associated flow rufc as uniqueness of solutions to boun- dary-v: In these models, the plastic yield function is defined in the effective configuration pertaining to the stresses in the undamaged material [ 57 — 9 ].
The plastic hardening rate is generally defined by the equivalent plastic strain, so the sum of the principal damage values in three directions: Substituting 44 into 6the relation between the second-order damage tensor and the compliance tensor of the damaged material can be given by By solving 45the reduction factor can be obtained. The variable K can be non-dimensionalized so that its cocrete value is unity. Substituting 29 into 27c and 27d yields the increments of the damage variables and.
Instead, they have found that the bulk modulus depends primarily on the volume strain, and the shear modulus on the plastic-damaye shear strain, n the elastic range.
In this algorithm, the damage and plastic corrector is along the normal at the elastic trial point, which avoids considering the intersection between the predicting increments of elastic stress and the damage surfaces.
In order that the value of K correspondins to the peak stress may be the same in the biaxial as in the uniaxial compression case.
A PLASTIC-DAMAGE MODEL FOR CONCRETE | ec pf –
Note that fftc 6, arc incfudcd among the z. View at Google Scholar.
To incorporate these modes into the formulation, the stress tensor is decomposed into forr positive part and negative part: The aim of the analytical investigation was to reveal the mechanism for the development of concrete cracking due to corrosion of reinforcement. The other set of singular points is of great importance because it includes biaxial and, as a special case.
A plastic-damage model for concrete to Experimental bond Fig.
In order words, while the yield surface however defined is closed. This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The expression for the increments of the plastic strain can be obtained by substituting 27b into Determination of Specific Functions For Concrete Specific functions for concrete are proposed based on the general framework of the coupled plastic damage model given in the previous section.
On the creep rupture of structures. By solving 45the reduction factor can be obtained. The effective damage tensor is given by Differentiation of the elastic thermodynamic moeel yields the strain-stress relations where is the component of the deviatoric tensor.
A Coupled Plastic Damage Model for Concrete considering the Effect of Damage on Plastic Flow
A constitutive relation for concrctc. Introduction The mechanical behavior of concrete is unique, due to the influence of micromechanisms involved in the nucleation and growth of microcracks and plastic flow.
The specific expressions of and are given as where and are, respectively, the initial damage energy release threshold under tension and compression, and are the parameters controlling the damage evolution rate under tension, and and are the parameters controlling the damage evolution lublinsr under compression. Numeri- cal results obtained for the T: The model parameters obtained from the experimental data [ 31 ] are listed in Table 1.
The specific reduction factor is defined as the sum of the principal values of a second-order damage tensor, which is deduced from the compliance tensor of the damaged material.